507 Mechanical Movements

98

Irregular vibrating motion is produced by the rotation of the…

Irregular vibrating motion is produced by the rotation of the circular disk, in which is fixed a crank-pin working in an endless groove cut in the vibrating arm.

Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.

Modelled as
The disk (the only driven joint, 20 rpm) carries a crank-pin 4 cm from its centre. The vibrating arm hangs on a pivot 12 cm above the centre and is cut with an endless (closed) groove 1.04 cm wide along its length, in which the pin works by real contact. The pin carries the arm to the angle of the line from the pivot to the pin, swinging it 19.5 deg each way, quickest through the middle and slowest at the ends: an irregular vibration.
Measured
Arm angle against the disk: slopes -0.4987, +0.0984, +0.2499 and +0.1005 rad/rad at 0, 90, 180 and 270 deg against the ideal -0.4981, +0.0996, +0.2499 and +0.0996 (r2 0.9967-1.0000); swing -0.338..+0.338 rad (ideal 0.340). Max penetration 0.02 mm.
Notes
The groove is 2 hundredths clear of the pin each side; the arm hinge (damping 0.1) is the joint; the groove closes at both ends.

Film (MP4) · GIF · Still (PNG) · Spec (YAML) · Model (MJCF)

Figure 98 from Brown, 1868
Brown's figure 98 (1868)